Spectral properties of the discrete random displacement model

  • Roger Nichols

    The University of Tennessee at Chattanooga, USA
  • Günter Stolz

    University of Alabama at Birmingham, USA


We investigate spectral properties of a discrete random displacement model, a Schrödinger operator on 2(Zd)\ell^2(\Bbb Z^d) with potential generated by randomly displacing finitely supported single-site terms from the points of a sublattice of Zd\Bbb Z^d. In particular, we characterize the upper and lower edges of the almost sure spectrum. For a one-dimensional model with Bernoulli distributed displacements, we can show that the integrated density of states has a 1/log21/\log^2-singularity at external as well as internal band edges.

Cite this article

Roger Nichols, Günter Stolz, Spectral properties of the discrete random displacement model. J. Spectr. Theory 1 (2011), no. 2, pp. 123–153

DOI 10.4171/JST/6